Sr Examen

Otras calculadoras

(arcsin((2x)^1/2))/(5cosx+3^x)
Derivada de la función/ arcsin((2x)^1/2)/ (arcsin((2x)^1/2))/(5cosx+3^x)

Derivada de (arcsin((2x)^1/2))/(5cosx+3^x)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /  _____\
asin\\/ 2*x /
-------------
            x
5*cos(x) + 3
asin⁡(2x)3x+5cos⁡(x)\frac{\operatorname{asin}{\left(\sqrt{2 x} \right)}}{3^{x} + 5 \cos{\left(x \right)}} 
asin(sqrt(2*x))/(5*cos(x) + 3^x)
Gráfica
02468-8-6-4-2-10100.00.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/            x       \     /  _____\                    ___               
\5*sin(x) - 3 *log(3)/*asin\\/ 2*x /                  \/ 2                
------------------------------------ + -----------------------------------
                         2                 ___   _________ /            x\
          /            x\              2*\/ x *\/ 1 - 2*x *\5*cos(x) + 3 /
          \5*cos(x) + 3 /
(−3xlog⁡(3)+5sin⁡(x))asin⁡(2x)(3x+5cos⁡(x))2+22x1−2x(3x+5cos⁡(x))\frac{\left(- 3^{x} \log{\left(3 \right)} + 5 \sin{\left(x \right)}\right) \operatorname{asin}{\left(\sqrt{2 x} \right)}}{\left(3^{x} + 5 \cos{\left(x \right)}\right)^{2}} + \frac{\sqrt{2}}{2 \sqrt{x} \sqrt{1 - 2 x} \left(3^{x} + 5 \cos{\left(x \right)}\right)}
Simplificar
Segunda derivada [src] 
/                                                 2\                                                                         
|                          /             x       \ |                                                                         
|            x    2      2*\-5*sin(x) + 3 *log(3)/ |     /  _____\                                                           
|5*cos(x) - 3 *log (3) + --------------------------|*asin\\/ 2*x /     ___ /1      2    \                                    
|                               x                  |                 \/ 2 *|- + --------|       ___ /             x       \  
\                              3  + 5*cos(x)       /                       \x   -1 + 2*x/     \/ 2 *\-5*sin(x) + 3 *log(3)/  
------------------------------------------------------------------ - -------------------- - ---------------------------------
                           x                                             ___   _________      ___   _________ / x           \
                          3  + 5*cos(x)                              4*\/ x *\/ 1 - 2*x     \/ x *\/ 1 - 2*x *\3  + 5*cos(x)/
-----------------------------------------------------------------------------------------------------------------------------
                                                         x                                                                   
                                                        3  + 5*cos(x)
(−3xlog⁡(3)2+5cos⁡(x)+2(3xlog⁡(3)−5sin⁡(x))23x+5cos⁡(x))asin⁡(2x)3x+5cos⁡(x)−2(22x−1+1x)4x1−2x−2(3xlog⁡(3)−5sin⁡(x))x1−2x(3x+5cos⁡(x))3x+5cos⁡(x)\frac{\frac{\left(- 3^{x} \log{\left(3 \right)}^{2} + 5 \cos{\left(x \right)} + \frac{2 \left(3^{x} \log{\left(3 \right)} - 5 \sin{\left(x \right)}\right)^{2}}{3^{x} + 5 \cos{\left(x \right)}}\right) \operatorname{asin}{\left(\sqrt{2 x} \right)}}{3^{x} + 5 \cos{\left(x \right)}} - \frac{\sqrt{2} \left(\frac{2}{2 x - 1} + \frac{1}{x}\right)}{4 \sqrt{x} \sqrt{1 - 2 x}} - \frac{\sqrt{2} \left(3^{x} \log{\left(3 \right)} - 5 \sin{\left(x \right)}\right)}{\sqrt{x} \sqrt{1 - 2 x} \left(3^{x} + 5 \cos{\left(x \right)}\right)}}{3^{x} + 5 \cos{\left(x \right)}}
Simplificar
Tercera derivada [src] 
  /                                                 3                                                     \                                                                                                                                                                        
  |                          /             x       \      /             x    2   \ /             x       \|                                                                   /                                                 2\                                                 
  |            x    3      6*\-5*sin(x) + 3 *log(3)/    6*\-5*cos(x) + 3 *log (3)/*\-5*sin(x) + 3 *log(3)/|     /  _____\                                                     |                          /             x       \ |                                                 
  |5*sin(x) + 3 *log (3) + -------------------------- - --------------------------------------------------|*asin\\/ 2*x /     ___ /3         12            4      \       ___ |            x    2      2*\-5*sin(x) + 3 *log(3)/ |                                                 
  |                                            2                           x                              |                 \/ 2 *|-- + ----------- + ------------|   3*\/ 2 *|5*cos(x) - 3 *log (3) + --------------------------|       ___ /1      2    \ /             x       \
  |                             / x           \                           3  + 5*cos(x)                   |                       | 2             2   x*(-1 + 2*x)|           |                               x                  |   3*\/ 2 *|- + --------|*\-5*sin(x) + 3 *log(3)/
  \                             \3  + 5*cos(x)/                                                           /                       \x    (-1 + 2*x)                /           \                              3  + 5*cos(x)       /           \x   -1 + 2*x/                        
- ----------------------------------------------------------------------------------------------------------------------- + --------------------------------------- + ------------------------------------------------------------ + ----------------------------------------------
                                                        x                                                                                 ___   _________                             ___   _________ / x           \                         ___   _________ / x           \      
                                                       3  + 5*cos(x)                                                                  8*\/ x *\/ 1 - 2*x                          2*\/ x *\/ 1 - 2*x *\3  + 5*cos(x)/                     4*\/ x *\/ 1 - 2*x *\3  + 5*cos(x)/      
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                    x                                                                                                                                              
                                                                                                                                   3  + 5*cos(x)
−(3xlog⁡(3)3+5sin⁡(x)−6(3xlog⁡(3)−5sin⁡(x))(3xlog⁡(3)2−5cos⁡(x))3x+5cos⁡(x)+6(3xlog⁡(3)−5sin⁡(x))3(3x+5cos⁡(x))2)asin⁡(2x)3x+5cos⁡(x)+2(12(2x−1)2+4x(2x−1)+3x2)8x1−2x+32(3xlog⁡(3)−5sin⁡(x))(22x−1+1x)4x1−2x(3x+5cos⁡(x))+32(−3xlog⁡(3)2+5cos⁡(x)+2(3xlog⁡(3)−5sin⁡(x))23x+5cos⁡(x))2x1−2x(3x+5cos⁡(x))3x+5cos⁡(x)\frac{- \frac{\left(3^{x} \log{\left(3 \right)}^{3} + 5 \sin{\left(x \right)} - \frac{6 \left(3^{x} \log{\left(3 \right)} - 5 \sin{\left(x \right)}\right) \left(3^{x} \log{\left(3 \right)}^{2} - 5 \cos{\left(x \right)}\right)}{3^{x} + 5 \cos{\left(x \right)}} + \frac{6 \left(3^{x} \log{\left(3 \right)} - 5 \sin{\left(x \right)}\right)^{3}}{\left(3^{x} + 5 \cos{\left(x \right)}\right)^{2}}\right) \operatorname{asin}{\left(\sqrt{2 x} \right)}}{3^{x} + 5 \cos{\left(x \right)}} + \frac{\sqrt{2} \left(\frac{12}{\left(2 x - 1\right)^{2}} + \frac{4}{x \left(2 x - 1\right)} + \frac{3}{x^{2}}\right)}{8 \sqrt{x} \sqrt{1 - 2 x}} + \frac{3 \sqrt{2} \left(3^{x} \log{\left(3 \right)} - 5 \sin{\left(x \right)}\right) \left(\frac{2}{2 x - 1} + \frac{1}{x}\right)}{4 \sqrt{x} \sqrt{1 - 2 x} \left(3^{x} + 5 \cos{\left(x \right)}\right)} + \frac{3 \sqrt{2} \left(- 3^{x} \log{\left(3 \right)}^{2} + 5 \cos{\left(x \right)} + \frac{2 \left(3^{x} \log{\left(3 \right)} - 5 \sin{\left(x \right)}\right)^{2}}{3^{x} + 5 \cos{\left(x \right)}}\right)}{2 \sqrt{x} \sqrt{1 - 2 x} \left(3^{x} + 5 \cos{\left(x \right)}\right)}}{3^{x} + 5 \cos{\left(x \right)}}
Simplificar
Gráfico
Derivada de (arcsin((2x)^1/2))/(5cosx+3^x)
    © Sr Examen – Калькулятор